Question

Arthur Meiners is the production manager of? Wheel-Rite, a small producer of metal parts.? Wheel-Rite supplies? Cal-Tex, a larger assembly? company, with 10 comma 400 wheel bearings each year. This order has been stable for some time. Setup cost for? Wheel-Rite is ?$38?, and holding cost is ?$0.60 per wheel bearing per year.? Wheel-Rite can produce 450 wheel bearings per day.? Cal-Tex is a? just-in-time manufacturer and requires that 47 bearings be shipped to it each business day. ?a) What is the optimum production? quantity? 1213 units ?(round your response to the nearest whole? number). ?b) What is the maximum number of wheel bearings that will be in inventory at? Wheel-Rite? 1086 units ?(round your response to the nearest whole? number). ?c) How many production runs of wheel bearings will? Wheel-Rite have in a? year? 8.57 runs ?(round your response to two decimal? places). ?d) What is the total setup plus holding cost for? Wheel-Rite? ?$ nothing ?(round your response to two decimal? places).

Answer 1

Annual demand, D = 10400

Demand rate, d = 47 per day

Production rate, p = 450 per day

Setup cost, S = $ 38

Holding cost, H = $ 0.6

a) Optimum production quantity (as per EPQ model) = SQRT(2DS/(H*(1-d/p)))

= SQRT(2*10400*38/(0.6*(1-47/450)))

= 1213 units

b) Maximum number of wheel bearings in inventory = Q*(1-d/p) = 1213*(1-47/450) = 1086 units

c) Number of Production runs in a year = D/Q = 10400/1213 = 8.57 runs

d) Total setup cost plus holding cost = (D/Q)*S + (Q/2)*H*(1-d/p) = (10400/1213)*38 + (1213/2)*0.6*(1-47/450) = $ 651.70